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Đáp án+Giải thích các bước giải:

`a)`

`2-x=2(x-2)^3`

`=>(2-x)+2(2-x)^3=0`

`=>(2-x)[1+2(2-x)^2]=0`

`=>(2-x)[1+2(4-4x+x^2)]=0`

`=>(2-x)(1+8-8x+2x^2)=0`

`=>(2-x)(2x^2-8x+9)=0`

Vì `2x^2-8x+9=2(x^2-4x+9/2)=2(x-2)^2+1>=1>0AA`

`=>2-x=0`

`=>x=2`

Vậy `x=2`

`b)`

`8x^3-72x=0`

`=>8x(x^2-9)=0`

`=>8x(x-3)(x+3)=0`

`=>[(x=0),(x-3=0),(x+3=0):}`

`=>[(x=0),(x=3),(x=-3):}`

Vậy `x\in{-3;0;3}`

`c)`

`(x-1,5)^6+2(1,5-x)^2=0`

`=>(x-1,5)^6+2(x-1,5)^2=0`

`=>(x-1,5)^2[(x-1,5)^4+2]=0`

Vì `(x-1,5)^4>=0AAx=>(x-1,5)^4+2>=2>0AAx`

`=>(x-1,5)^2=0`

`=>x-1,5=0`

`=>x=1,5`

Vậy `x=1,5`

`d)`

`2x^3+3x^2+3+2x=0`

`=>(2x^3+3x^2)+(2x+3)=0`

`=>x^2(2x+3)+(2x+3)=0`

`=>(2x+3)(x^2+1)=0`

Vì `x^2>=0AAx=>x^2+1>=1>0AAx`

`=>2x+3=0`

`=>2x=-3`

`=>x=-3/2`

Vậy `x=-3/2`

`e)`

`x^2(x+1)-x(x+1)+x(x-1)=0`

`=>[x^2(x+1)-x(x+1)]+x(x-1)=0`

`=>(x+1)(x^2-x)+x(x-1)=0`

`=>x(x+1)(x-1)+x(x-1)=0`

`=>(x-1)[x(x+1)+x]=0`

`=>(x-1)(x^2+x+x)=0`

`=>(x-1)(x^2+2x)=0`

`=>x(x-1)(x+2)=0`

`=>[(x=0),(x-1=0),(x+2=0):}`

`=>[(x=0),(x=1),(x=-2):}`

Vậy `x\in{-2;0;1}`

`f)`

`x^3-4x-14x(x-2)=0`

`=>(x^3-4x)-14x(x-2)=0`

`=>x(x^2-4)-14x(x-2)=0`

`=>x(x-2)(x+2)-14x(x-2)=0`

`=>(x-2)[x(x+2)-14x]=0`

`=>(x-2)(x^2+2x-14x)=0`

`=>(x-2)(x^2-12x)=0`

`=>x(x-2)(x-12)=0`

`=>[(x=0),(x-2=0),(x-12=0):}`

`=>[(x=0),(x=2),(x=12):}`

Vậy `x\in{0;2;12}`

`#ld`